Correct Answer: C. 2x - y = -5

Explanation

Condition for Parallelism means that their gradient value is same

line 2x - y = 5 is rearranged

As y = 2x - 5 from y = mx + c

: line 2x - y = 5 has the gradient of 2

A parallel line with gradient of 2 and intercept of 5

→ 2x - y = -5

Rearranged as y = 2x + 5

Correct Answer: A. N2,050

Correct Answer: C. \(\frac{7}{40}\)

Explanation

\(\frac{5}{8} - \frac{3}{4} ÷ \frac{5}{12} x \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{3}{4} ÷ \frac{5}{12}) \times \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{3}{4} \times \frac{12}{5}) \times \frac{1}{4}\)

⇒ \(\frac{5}{8} - (\frac{9}{5} \times \frac{1}{4})\)

⇒ \(\frac{5}{8} - \frac{9}{20}\)

∴ \(\frac{7}{40}\)

Correct Answer: D. 1.01

Explanation

The probability not scoring 85% is = 1 - pro(scoring 85%)

= 1 - \(\frac{85}{100}\) = 1 - 0.85

= 0.15

not scoring would be less than 1

Explanation

(b) If we let r be the retardation, then \(\frac{s}{t}\) : r = 3 : 4

when simplified, r = \(\frac{10}{3}\)

Velocity after 4 seconds = 20 + \(\frac{5}{2}\) x 4 = 30ms\(^{-1}\)

So that \(\frac{5}{2}\) : \(\frac{30}{t}\) = \(\frac{3}{4}\)

t = 9 seconds

(c) The total distance of the journey = {[\(\frac{1}{2}\) (20 + 30)4] + (30 x 8) + \(\frac{1}{2}\)(30 x 9)}

= 100 + 240 + 135 = 475 metres

Explanation

(a)

Given : Circle ABC, centre O.

To prove: < AOB = < ACB

Construction : Join CO produced to P.

Proof: With the lettering in the figure, OA = OB (radii)

\(x_{1} = x_{2}\) (base angles of isosceles triangle)

\(\therefore < AOP = x_{1} + x_{2}\) (exterior angle of triangle AOC)

\(\therefore < AOP = 2x_{2} (x_{1} = x_{2})\) (base angles of an isosceles triangle)

Similarly, \(< BOP = 2y_{2}\)

\(\therefore < AOB = 2x_{2} + 2y_{2} \)

= \(2(x_{2} + y_{2})\)

\(\implies < AOB = 2 \times < ACB\) (proved)

(b) From the figure, \(< ACB = \frac{130°}{2} = 65°\) (angle subtended at the centre of the circle)

\(< ACO = 26°\) (Base angles of isosceles triangle ACO)

\(\therefore < BCO = 65° - 26° = 39°\)

\(< OBC = 39°\) (base angles of isosceles triangle OBC)

\(\therefore < COB = 180° - (39° + 39°) = 102°\)

Correct Answer: C. \(\frac{5!}{2!3!}\)

Correct Answer: A. 7y + 4x + 5 = 0

Correct Answer: D. \(85^o\)

Explanation

x + 2x + 2x + (x + \(30^o\)) + (x + \(20^o\)) + (x - \(10^o\)) = (2n - 4) x \(90^o\)

8x + 50 \(^o\) - 10\(^o\) = (2 x 6 -4) x 90\(^o\)

8x + 40\(^o\) = 8 x 90\(^o\) = 720\(^o\)

8x = 720\(^o\) - 40\(^o\) = 680\(^o\)

x = \(\frac{680^o}{8}\)

= 85\(^o\)

Correct Answer: D. 75